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When multiplying numbers in exponent notation with the same base, we can add the exponents.

Consider:

a2 × a3 = (a × a) × (a × a × a)
= a2 + 3
= a5

This is the first law of exponents:
am × an = am + n

Example:

a) 33 × 32
b) x5 × x3

Solution:

a) 33 × 32 = 33 + 2
= 35
b) x5 × x3 = x5 + 3
= x8

Common Error : The first law of exponents does NOT apply to addition of numbers in exponent notation.

am + an ≠ am + n

Scroll down the page for more examples and solutions of the first law of exponents and also the other laws of exponents.

Index rules - add and subtract indices
Basic look at the first two index laws
Properties of Exponents
The Product Rule: am × an = am + n
The Quotient Rule: am ÷ an = am - n
The Power Rule: (am)n = amn
Example:
Simplify
(3ab4)(2a2b)3
(x2y4/2xz)3
(2a4)(511)

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